Communications in Mathematical Physics

, Volume 187, Issue 1, pp 227–241 | Cite as

Differentiation of SRB States

  • David Ruelle

Dedicated to Klaus Hepp and Walter Hunziker for their 60th birthdays.

Abstract:Let f be a diffeomorphism of a manifold M, and ρf a (generalized) SRB state for f. If supp ρf is a hyperbolic compact set we show that the map \(\) is differentiable in a suitable functional setup, and we compute the derivative. When supp ρf is an attractor, the derivative is given by
$$$$
where X is the vector field \(\) . This formula can be extended to time dependent situations and also, at least formally, to nonuniformly hyperbolic situations.

The above results will find their use in the study of the Onsager reciprocity relations and the fluctuation-dissipation formula of nonequilibrium statistical mechanics.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • David Ruelle
    • 1
  1. 1.IHES, 91440 Bures sur Yvette, France, E-mail: ruelle@ihes.fr, and¶Math. Dept., Rutgers University, New Brunswick, NJ 08903, USAFR

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